H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function. Issue 13 (September 2019) - Li, Panshuo; Li, Pengxu; Liu, Yun; Bao, Hong; Lu, Renquan
Abstract: In this paper, the H ∞ control problem of periodic piecewise systems with polynomial time-varying subsystems is addressed. Based on a periodic Lyapunov function with a continuous time-dependent Lyapunov matrix polynomial, the H ∞ performance is studied. The result can be easily reduced to the conditions for periodic piecewise systems with constant subsystems or linear time-varying systems based on a common Lyapunov function or a linear time-varying Lyapunov matrix. Moreover, an H ∞ controller with time-varying polynomial controller gain is proposed as well, which could be directly solved with the linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the proposed method.